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The Voronoi diagram in structural optimisation

Friedrich, E.; (2008) The Voronoi diagram in structural optimisation. Masters thesis , UCL (University College London). Green open access

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Abstract

In the course of the exploration of computational means in the architectural design process, in order to investigate more complex, adaptive geometries, the Voronoi diagram has recently gained some attention, as a structure that is modular but not repetitive, with potential for a great variety of complex geometries. The project looks at the Voronoi diagram as a load-bearing structure, whether its formal potential can be useful for statical optimisation, and how this optimisation can be facilitated. Hereby, the edges of the Voronoi polyhedra are regarded as structural members of a statical system, which then is assessed by structural analysis software. The project explores different techniques to optimise the cell structure in regards to its structural properties. It is suggested that the main challenge to optimise the polyhedra structure lies in the inherent complex relationship between the Voronoi cell cores and the resulting cell geometry. Cell geometries emerge from combinatorial properties of the underlying set of points and so there is no means to manipulate the cells directly. Results seem to indicate that the emergent Voronoi polyhedra structure, although difficult to control due to its complex behaviour, can produce a very specific type of structural order, which is distinctively beneficial for a statical structure. Certain polyhedra structures which emerge from the Voronoi system appear to exhibit ‘synergetic’ system behaviour of cooperating tear and pressure forces, which makes the structure more stable and minimises deformation. The overall shape of the structure hereby is minimally transformed. The working principle of the optimised structure lies rather in how forces are redirected in the system due to its specific topology, rather than through geometrical transformations of the structure’s overall shape.

Type: Thesis (Masters)
Title: The Voronoi diagram in structural optimisation
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Approved for UCL Eprints by Mr A. Turner, Bartlett School of Graduate Studies
UCL classification: ?? BG ??
URI: http://discovery.ucl.ac.uk/id/eprint/14631
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